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Finding the Third Proportional to 235,829 and 509,006

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Solution

The third proportional to 235,829 and 509,006 is: 1,098,622.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    235,829 : 509,006 = 509,006 : x
  2. Step 2: Convert to fraction form
    235,829/509,006 = 509,006/x
  3. Step 3: Cross multiply
    235,829x = 509,006 × 509,006
  4. Step 4: Simplify right side
    235,829x = 259,087,108,036
  5. Step 5: Solve for x
    x = 259,087,108,036/235,829
  6. Step 6: Final answer
    x = 1,098,622.76

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.